pub fn new_birthday_probability(n: u32) -> f64 {
    let mut upper = 1 as f64;
    let mut lower = 1 as f64;
    for i in 0..n {
        upper *= 365 as f64 - i as f64;
        lower *= 365 as f64;
    }
    return 1 as f64 - (upper as f64) / (lower as f64);
}
